Sometimes a liquid (pure water in a clean vessel, for example) may be cooled below its freezing point without freezing. This is called undercooling. When a substance is dissolved in water, the freezing point of the solution is lower than that of pure water.

When a vapor in contact with its liquid has reached its maximum density, it is said to be saturated. The pressure of a saturated vapor can be changed only by a change in its temperature.

The boiling of any liquid takes place at a definite temperature for a definite pressure. An increase of pressure raises the boiling point, and a decrease lowers it. Boiling takes place at that temperature at which the pressure of the saturated vapor is equal to the pressure on the surface of the liquid.

Since the pressures of the saturated vapors of different liquids at the same temperature are different, it follows that the temperatures at which the pressures of saturated vapors will be equal to atmospheric pressure are different for different liquids. Hence the temperatures of their boiling points are different.

The heat of vaporization is equal to the number of calories of heat required to change 1 gram of liquid into vapor without any temperature change. The heat of vaporization of water at 100° C. is 539 calories per gram.

Evaporation is a cooling process; condensation, a heating process. Water may be frozen by its evaporation. At the triple point a liquid may freeze and boil at the same time.

At a temperature higher than its critical temperature no substance can exist in liquid form, no matter what the pressure may be.

The cooling effect of the evaporation and expansion of ammonia is used in refrigeration. In a liquid-air machine the cooling due to the free expansion of compressed air is utilized.

PROBLEMS

1. 25 gm. of ice at 0° C. are added to 400 gm. of water at 40° C. Compute the resulting temperature.

2. 200 gm. of water at a temperature of 30° C. are poured into a cavity in a block of ice at 0° C. How much ice should be melted?

3. A bullet of mass 9 gm. and having a speed of 700 m./sec. is shot into a block of ice. If the bullet before entering was at the temperature of the ice, 0° C., how much ice should be melted by the energy of the bullet?

4. A minute crystal of ice is dropped into 160 gm. of water which has been undercooled to -5° C. The temperature immediately rises to 0° С. How much ice will be formed?

5. A liter of water (1000 gm.) is cooled from 80° C. to a final temperature of 20° C. by adding snow and by stirring. How much snow is required?

6. In a determination of the specific heat of iron a mass of 160 gm. was heated to 100° C. and dropped into a cavity in a block of ice. The mass of ice melted was 22.4 gm. Compute the specific heat of iron.

7.250 gm. of ice at 0° C. are dropped into a copper calorimeter the thermal capacity of which is 18 and which contains 400 gm. of water at 60° C. Find the resulting temperature.

8. A mass of 400 gm. of copper (specific heat 0.093) is heated in an oil bath and then placed in a cavity in a block of ice. The mass of ice melted is 75 gm. Required to find the temperature of the bath.

✓ 9.1 kg. of lead (specific heat 0.031) is dropped into a vessel (thermal capacity 20) which contains 200 gm. of water and 50 gm. of ice at 0° C. The initial temperature of the lead is 300° C. Find the temperature of the mixture.

✓ 10. How many calories are required to change 50 gm. of water at 50° С. to steam at 100° C.?

11.30 gm. of steam at 100° C. are passed into a cavity in a large block of ice at 0° C. How many grams of ice will be melted?

12. A calorimeter (specific heat 0.093) which has a mass of 90 gm. contains 391 gm. of water at 5° C. 20 gm. of steam are forced in, and the temperature becomes 35° C. Compute the heat of vaporization of the water.

13. 10 gm. of steam at 100° C. and 50 gm. of ice at 0° C. are added to 400 gm. of water at 30° C., contained in a 200-gram copper calorimeter. Compute the final temperature of the mixture. (The specific heat of copper is 0.09.)

14. 40 gm. of ice at 0° C. and 10 gm. of steam at 100° C. are added to a 100-gram copper calorimeter containing 300 gm. of water at 20° C. Find the resulting temperature. (The specific heat of copper is 0.09.)

15. Compute the number of heat units required to raise 20 gm. of ice at -15° C. to steam at 150° C. (The specific heat of both steam and ice is 0.5.)

16. What amount of steam at 100° C. must be passed into 16 kg. of water at 0° C., in which 4 kg. of ice are floating, in order to raise the whole to 30° C.?

CHAPTER XXII

SOME APPLICATIONS TO METEOROLOGY

Dew and frost, 288. Experimental methods of finding the dew point, 289. Humidity, 290. Methods of measuring humidity, 291. Fog and cloud, 292. Rain or snow, 293. Conditions causing clouds or rain, 294. Winds: general causes, 295. Effect of the rotation of the earth, 296. Cyclones, 297. Anticyclones, 298. Effect of cyclones and anticyclones on the weather, 299. Thunderstorms, 300. Tornadoes, 301. The averaging of temperature, 302. The averaging of rainfall, 303.

The science of meteorology deals with those phenomena of the atmosphere which affect our weather. To a very large extent it is a series of applications of the principles of physics to these special problems. So true is this that meteorology has been defined as the physics of the atmosphere. Obviously in a text of this kind it would be out of place to attempt to cover much of this important and extensive subject. However, some of the more commonly observed phenomena, which are excellent illustrations of principles explained in this book, will be given in this chapter.

288. Dew and frost. When cold water is poured into a glass on a warm, humid day, the vapor in the air near the glass will condense on the glass, provided the temperature of the cold water is low enough to cool the air next to the glass below the point at which the water vapor in the air becomes saturated. At night, objects near the ground frequently cool by radiation until they are colder than the air, and water vapor of the air condenses on them in the form of dew or frost.

The pressure of saturated water vapor at 0° C. is 0.46 centimeter of mercury. When the air contains water vapor the pressure of which is less than 0.46 centimeter, the vapor must be cooled to some temperature below the freezing point before it will be saturated. If it came in contact with some body of sufficiently low temperature so that some of the vapor condensed on the body, it would not form drops of water but would form frost.

The dew point of the atmosphere is defined as that temperature to which it must be lowered in order that the water vapor which it contains should become saturated. If the pressure of the water vapor in the air is 0.92 centimeter, then, no matter what the temperature of the air may be, its dew point is 10° C., or 50° F. For at this temperature (see the table on page 296) water vapor at a pressure of 0.92 centimeter is saturated.* When the dew point is below freezing, it is often called the frost point.

Dew or frost collects on objects if their temperature goes below the dew point of the air. In cold weather water or frost often collects on the inside of our windows. This is because the temperature of the glass is below the dew point of the air in the house. If dew or frost does not collect on the windows in severe winter weather, it usually indicates that the air in the house is very dry, with a low dew point.

289. Experimental methods of finding the dew point. The following is a very simple method for finding the dew point: A thinwalled polished metallic cup, a thermometer, and some ice water are needed. Water is poured into the cup, and its temperature is gradually lowered by adding small quantities of ice water while stirring thoroughly. When a film of moisture begins to appear on the cup, the thermometer is read. Then the temperature of the cup is allowed to rise slowly. When the film begins to evaporate, the temperature is read again. The mean of these two readings gives the dew point. The more slowly the temperature is lowered in the neighborhood of the dew point, the more accurately can the dew point be determined. Practically all the direct methods are modifications of this simple one. The dew point is usually obtained in meteorological stations from the readings of the wet-bulb and dry-bulb thermometers. This purely empirical method will be explained later.

290. Humidity. The absolute humidity of the atmosphere is defined as the mass of water vapor present in a unit volume. Usually the humidity is expressed in grams per cubic meter or in grains per cubic foot. The amount of water vapor present in the air varies a great deal, depending on the temperature and degree of saturation. When air is at a temperature of 0° C., and the water vapor is saturated, there are about 4.8 grams per cubic meter; but if the temperature is 30° C. (86° F.), and the amount of water vapor is only half of that required to produce saturation, there will be about 15 grams per cubic meter (see the table on page 296). We are usually much more interested in what we sometimes call the dampness of the air. This is a relative term, depending on the degree of saturation. For example, if the air temperature is 0° C. and there are 4.7 grams per cubic meter of water vapor present, it is a very damp day; but if the temperature were 30° C. (86° F.) = and there were only 4.7 grams per cubic meter of water vapor present, it would be an extremely dry day, for at that temperature it requires about 30 grams of water vapor per cubic meter to produce saturation (see the table on page 296). The scientific term for stating the relative dampness of the air is relative humidity. The relative humidity is defined as the ratio of the absolute humidity to that required to produce saturation.

Since the mass of water vapor present in the air is closely proportional to the pressure of the vapor, it follows, approximately, that, for any definite temperature,

Mass of vapor per cu. m.

Mass of saturated vapor per cu. m.

pressure of vapor

pressure of saturated vapor

Hence the relative humidity may also be defined as the ratio of the pressure of the vapor in the air to the pressure that would be exerted by a saturated vapor at the same temperature.

291. Methods of measuring humidity. 1. The absolute humidity of the air can be obtained by drawing a known volume of air through a series of tubes containing calcium chloride or some other substance which absorbs water vapor. These tubes are weighed before and after the air is drawn through. The increase in the mass of the tubes gives the mass of water vapor absorbed.